(2021.7) 分子のグラフ表現と機械学習の最近

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1
ichigaku.takigawa@riken.jp
33 AIP Open Seminar
2021 7 14

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2
https://itakigawa.github.io/
ͨ ͖ ͕ Θ ͍ ͪ ͕ ͘

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3
CC1CCNO1
Representation
Learning
…
NCc1ccoc1.S=(Cl)Cl>>[RX_5]S=C=NCc1ccoc1
Task-Speciﬁc
Head

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4
Amide
module
Proline
module
Oxazoline
module
Phenyl
Carboxyl
Methyl
Tert-butyl
Isoprophyl
Trifluoromethyl
Benzyl
J.J.Sylvester, Chemistry and Algebra, Nature, 17:284 (1878).
GDB-11 (Fink+, JCIM 2007) C,N,O,F,ʹΑΔ11‫ࢠݪ‬ҎԼͷ෼ࢠͷશྻ‫ڍ‬ (2640ສ)
GDB-13 (Blum+, JACS 2009) C,N,O,S,ClʹΑΔ13‫ࢠݪ‬ҎԼͷ෼ࢠͷશྻ‫ڍ‬ (9ԯ7700ສ)
GDB-17 (Ruddigkeit+, JCIM 2012) C,N,O,S,ϋϩήϯʹΑΔ17‫ࢠݪ‬ҎԼͷ෼ࢠͷશྻ‫ڍ‬ (1,664ԯ)
Hydrogen
Proline
Oxazoline
Amide
Ethyl
Cyclohexyl adamantyl
ʹ͸༷ʑͳஔ‫͕ج׵‬ೖΕΒΕΔ

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5
https://pubchem.ncbi.nlm.nih.gov/#query=C12CC(C(CC1)C2)C
‫ີݫ‬Ұக‫ࡧݕ‬
Norbornane
ྨࣅੑ‫ࡧݕ‬ ্෦ߏ଄‫ࡧݕ‬
෦෼ߏ଄‫ࡧݕ‬ ཱମྨࣅੑ‫ࡧݕ‬
ΫΤϦߏ଄ͱಉ͡ ΫΤϦͱྨࣅ ΫΤϦߏ଄ʹ‫·ؚ‬ΕΔ
ΫΤϦߏ଄Λ‫ؚ‬Ή ΫΤϦߏ଄ͱཱମతʹྨࣅ

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6
https://www.molgen.de/online.html
EXAMPLE 5: Generate all (theoretically possible)
structures of mass ≤ 40 with elements, C, H, N3, O
Hu, Stumpfe, Bajorath, J Med Chem (2016) https://doi.org/10.1021/acs.jmedchem.5b01746
Liu, Naderi, Alvin, Mukhopadhyay, Brylinski, JCIM (2017) https://doi.org/10.1021/acs.jcim.6b00596

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7
O
N
N
N
H
NH
N
N
N
CH3
CH3
https://en.wikipedia.org/wiki/Molecular_dynamics

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8
<latexit sha1_base64="dwtAUUE0cfsFu6+2FLg7b109CNE=">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</latexit>
✓i
<latexit sha1_base64="tkPRNIYeS8tNgbH62CO/ULi3LDw=">AAACi3ichVHLSsNAFL2Nr/quuhHcBIviqtykoa3iQhTBZbXWFtpSkjjaaF4k04IWf8ClGxe6UXAhfoAf4MYfcOEniMsKblx4k0bEhXrDZO6cuefOmTmaaxo+R3yOCT29ff0D8cGh4ZHRsfHExOSO7zQ9nRV1x3S8sqb6zDRsVuQGN1nZ9ZhqaSYraYdrwX6pxTzfcOxtfuSymqXu28aeoaucoHKVNxhX6wf1RBJTi7mMrGRETCFmJVkKEjmrpBVRIiSIJESRdxL3UIVdcECHJljAwAZOuQkq+PRVQAIEl7AatAnzKDPCfQYnMETcJlUxqlAJPaT/Pq0qEWrTOujph2ydTjFpeMQUYQ6f8BY7+Ih3+IIfv/Zqhz0CLUc0a10uc+vjp9OF939ZFs0cGt+sPzVz2INcqNUg7W6IBLfQu/zW8XmnsLQ1157Ha3wl/Vf4jA90A7v1pt9ssq2LP/RopIVejAz6ckH8PdmRU1ImJW8qyZXVyKo4zMAsLJAfWViBDchDMfThDC7gUhgV0sKSsNwtFWIRZwp+hLD+CU69k0E=</latexit>
✓j
https://en.wikipedia.org/wiki/Chirality_(chemistry)

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9
CH3
N
N
H
N
H
H3C
N
<latexit sha1_base64="tiacEhQgmTkomNeV5LHmrY6hmbk=">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</latexit>
x1
<latexit sha1_base64="4Sn0JXQ8Nli9zYaRMiYfd4a9JHg=">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</latexit>
x2
<latexit sha1_base64="4+jTZNjL3Gn2jlRZoSuvOUm3czc=">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</latexit>
.
.
.
<latexit sha1_base64="9bGzB58W461U5gZXfti9NDCxbbY=">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</latexit>
y
Hansch-Fujita QSAR
(Hammetଇͷੜ෺ֶ൛)
(Hammettఆ਺)
Hammettଇ
<latexit sha1_base64="Rtaf0NASFdmDpXAc2f6wWTFtSe0=">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</latexit>
log(K/KH) = ⇢
“Linear Free Energy
Relationships (LFERs)”
<latexit sha1_base64="Xiu9z9gQDsGsRYjNbuMpINCUhK0=">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</latexit>
log(1/C) = 1(log P)2
+ 2 log P + 3 + 4Es + Const.
(Taftఆ਺)
(෼഑܎਺)
ੜ෺‫׆‬ੑ΍
ೱ౓

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10
CH3
N
N
H
N
H
H3C
N
<latexit sha1_base64="tiacEhQgmTkomNeV5LHmrY6hmbk=">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</latexit>
x1
<latexit sha1_base64="4Sn0JXQ8Nli9zYaRMiYfd4a9JHg=">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</latexit>
x2
<latexit sha1_base64="4+jTZNjL3Gn2jlRZoSuvOUm3czc=">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</latexit>
.
.
.
<latexit sha1_base64="9bGzB58W461U5gZXfti9NDCxbbY=">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</latexit>
y
f

/ 41
11
Stumpfe and Bajorath, J Med Chem (2012) https://doi.org/10.1021/jm201706b
Activity cliffs Selectivity cliffs

/ 41
12
CH3
N
N
H
N
H
H3C
N
0.739
H3C
H3C
NH
O
N
O
N
O
CH3
O N
NH2
O
CH3
Br
CH3
N
H3C
H
N
S
N
O
CH3
N
OH
CH3
CH3
N
N
N
CH3
H3C
H2N NH2
‫ݟ‬ຊྫ͔ΒͷϓϩάϥϜੜ੒

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13
• Mutagenic potency
• Carcinogenic potency
• Endocrine disruption
• Growth inhibition
• Aqueous solubility
N
NH
O
O
H
H
H
H H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
O
O
O
O
O
O
Cl
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
Br
Br O P
O
O Br
Br
O
Br
Br
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
N
S
N
N
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
O
N
O
O
H
H
H
O
O
H
H
N
O
O
Cl
Cl
Cl
H
H
H
H
H
H H
N
O
O
H
H
H
H
H
H
H H
H
N
O
O
H
H
H
H
H
H
H
N
H
N
O
O
N
O
O
H
H
H
H
H
H
H
H
N
CH3
O
O
H
N Cl
Cl
Cl
Cl
Cl
H3C
O O
O
O
O
O
H3C
CH3
CH2
O
HN
O
O
NH
CH3
HO
OH
CH3
N
O
O
CH3
N
N
H
N
H
H3C
N
H3C
H3C
NH
O
N
O
N
O
CH3
O N
NH2
O
CH3
Br
CH3
N
H3C
H
N
S
N
O
CH3
N
OH
CH3
CH3
N
N
N
CH3
H3C
H2N NH2
H
OH
O
HO
CH3
H
H
O
CH3
H
O
O
H3C H
H
H
O
H3C
S
CH3
O
H
H
O
CH3
CH3
O
O
HO
H3C
H
HO
F
H
O
H3C
NH2
O
N
HO
H
O
O
H
H
O
O
O
H3C
O
O
O
CH3
O
CH3
H
O
CH3
H
O
O
CH3
H
H
N
H
N O
H3C
O
O
O

/ 41
15
=@<TRIPOS>MOLECULE
*****
13 13 0 0 0
SMALL
GASTEIGER
@<TRIPOS>ATOM
1 C -2.5458 -9.4750 0.0000 C.2 1 UNL1 0.3080
2 C -3.3708 -9.4750 0.0000 C.2 1 UNL1 0.2529
3 C -2.2875 -8.6917 0.0000 C.2 1 UNL1 0.3838
4 C -3.6208 -8.6917 0.0000 C.3 1 UNL1 0.2067
5 O -2.9583 -8.2042 0.0000 O.3 1 UNL1 -0.4441
6 C -4.3583 -8.3125 0.0000 C.3 1 UNL1 0.2245
7 O -1.5000 -8.4375 0.0000 O.2 1 UNL1 -0.2412
8 O -2.0583 -10.1417 0.0000 O.2 1 UNL1 -0.2764
9 O -3.8500 -10.1417 0.0000 O.2 1 UNL1 -0.2843
10 O -5.0500 -8.7542 0.0000 O.3 1 UNL1 -0.2164
11 O -3.6958 -7.0417 0.0000 O.3 1 UNL1 -0.2174
12 C -4.3958 -7.4875 0.0000 C.3 1 UNL1 0.2185
13 H -4.2083 -9.2667 0.0000 H 1 UNL1 0.0853
@<TRIPOS>BOND
1 2 1 2
2 3 1 1
3 4 2 1
4 5 3 1
5 6 4 1
6 7 3 2
7 8 1 1
8 9 2 1
9 6 10 1
10 11 12 1
11 12 6 1
12 4 13 1
13 5 4 1
OC[C@H](O)[C@H]1OC(=O)C(=C1O)O
CIWBSHSKHKDKBQ-JLAZNSOCSA-N
InChI=1S/C6H8O6/
c7-1-2(8)5-3(9)4(10)6(11)12-5/
h2,5,7-10H,1H2/t2-,5+/m0/s1
1
2
3
4
5
6
7 8
9
10
11
12
13
2
2 1
1
1
1
1
1
1
1
1
1
1
single
single
single
double
double
double
double
double
double
single
single
single
aromatic aromatic
aromatic
aromatic
aromatic
aromatic
Kekulé Form

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MDL MACCS Keys
ΑΓෳࡶͳߏ଄ಛ௃ύλʔϯΛ໢ཏͨ͠PubChem Fingerprint (881bit)ͳͲ΋
00000000000000000000000000000000000000000000000000001100
00000000000000000000000000000000010000100000000000000000
0100000100011101000101010001001111100010101011111111110
Aromatic Ring>1 [F,Cl,Br,I] Heterocycle
֤ߏ଄ಛ௃ͷ༗ແΛ
֤bit(0/1)ʹ
ECFP (Extended Connectivity Fingerprint)
00001000100011001011001000001000010
HashingͰ‫ݻ‬ఆ௕ͷ
bit string΁ม‫׵‬
֤ۙ๣ߏ଄ʹuniqueͳ
id൪߸Λׂ౰ͯΔ
https://docs.chemaxon.com/display/docs/extended-connectivity-ﬁngerprint-ecfp.md
୳ࡧ൒‫ܘ‬ͷ্‫ͱݶ‬Ϗοτ௕͸ύϥϝλ
…

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Implicit Hydrogens Explicit Hydrogens
Structural Formula
Atomic Invariants

/ 41
<latexit sha1_base64="9kTSgBYDa8jzBNKjMs5WyhQ5V3k=">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</latexit>
K ,
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0.1
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0 0 1 1 1 0
1 0 0 0 0 1
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⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋱
1 0 1 1 1 0
y

/ 41
19
Kashima Kernel (Kashima+ 2003)
Weisfeiler-Lehman Kernel (Shervashidze+ 2011)
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G1
<latexit sha1_base64="FUojSoBiuD8NhDGX50StN4VMT70=">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</latexit>
G2
1 1
2
2
2
3
3
4
4
5
5
1,4 1,4
2,35
2,45
2,3
3,245
3,245
4,1235
4,1135
5,234
5,234
1,4
1
6 6
8
9
7
10
10
12
11
13
13
6
…
…
…
…
2 1 1 1 1 2 0 1
1 2 3 4 5 6 7 8
1 2 1 1 1 1 1 0
Marginalized Kernel (Tsuda+ 2002)
R-Convolution Kernel (Haussler 1999)
R D
<latexit sha1_base64="wpyn9s0DvnQcyTF5k8mpdFbbQqA=">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</latexit>
K(G1, G2)

/ 41
20
<latexit sha1_base64="JQWY0sKtSB2gZKyDx03+dQGakWQ=">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</latexit>
{Gi}n
i=1
Wale N., Ning X., Karypis G. (2010) Trends in Chemical Graph Data Mining. In: Aggarwal C., Wang H. (eds) Managing and Mining Graph Data. Advances
in Database Systems, vol 40. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-6045-0_19

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21
Wu et al, MoleculeNet: a benchmark for molecular machine learning, Chem Sci (2017)
https://doi.org/10.1021/jm201706b
http://moleculenet.ai

/ 41
22
Quantitative Structure–Property Relationship Modeling of Diverse Materials Properties. Chem Rev, 2012, 112 (5), pp 2889–2919
• Descriptors
• Descriptors3D
• GraphDescriptors
• Fingerprints
• ChemicalFeatures
• ChemicalForceFields
rdkit.Chem
rdkit.ML.Descriptors
Todeschini and Consonni, Molecular Descriptors
for Chemoinformatics. Wiley‐VCH, 2009.
https://doi.org/10.1002/9783527628766

/ 41
23
CC1CCNO1
Representation
Learning
…
Task-Speciﬁc
Head

/ 41
24
N O
C
C
C
C
H
H
H
H
H
N O
C
C
C
C
H
H
H
H
H
(sum, mean or max)
+ attention
<latexit sha1_base64="WNEpfX6Bt3G9f3Toyi7bd0iGAgY=">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</latexit>
hi
0
@hi,
M
j2Ni
(hi, hi, eij)
1
A

/ 41
25
<latexit sha1_base64="g4+ASD58WMoop6pPZrlXxKmH4Ao=">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</latexit>
h
(l+1)
i
0
@h
(l)
i ,
M
j2Ni
cij (h
(l)
j )
1
A
(Kipf and Welling, ICLR ︎2017)
<latexit sha1_base64="/ysxkHppQdzDUyY3/GZwEdDJ/xs=">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</latexit>
M
<latexit sha1_base64="wzm3ilbAnfk/uMMoZ6aWms13YM8=">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</latexit>
G1
<latexit sha1_base64="FUojSoBiuD8NhDGX50StN4VMT70=">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</latexit>
G2
Xu, Hu, Leskovec, Jegelka, How powerful are graph neural networks? ICLR (2019)
Kipf and Welling, Semi-supervised classiﬁcation with graph convolutional networks. ICLR (2017)

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26
Duvenaud, Maclaurin, Aguilera-Iparraguirre, Gómez-Bombarell, Hirzel, Aspuru-Guzik, Adams,
Convolutional networks on graphs for learning molecular ﬁngerprints. NIPS (2015)

/ 41
27
<latexit sha1_base64="cBeKmO56fa7C7dRhqoeO+wzPccY=">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</latexit>
1
<latexit sha1_base64="M4MwU1uekvwiIbvhYrrTkZ2bkH0=">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</latexit>
2
<latexit sha1_base64="Q//0F9YqO0nHMYOeiEwv1elE5z4=">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</latexit>
3
<latexit sha1_base64="4Voo9nXZ704HCmfeaH1ujpbOOII=">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</latexit>
4
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6
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e1
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e2
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e3
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e4
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e0
1
e1
e2
e3
e4
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e0
1
out-edges
in-edges
aggregate
update
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1
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3
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4
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5 <latexit sha1_base64="wEoTiJwn0Vf/dExl2QfhhhWO3g0=">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</latexit>
6
e1
e2
e3
e4
e1
e2
e3
e4
in-edges
aggregate
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v1
concat
update
Directed MPNN (Dai et al, ICML 2016)
node
feature
ChemProp (Yang et al, JCIM 2019)
https://github.com/chemprop/chemprop
Stokes et al, Cell (2020) https://doi.org/10.1016/j.cell.2020.01.021
Marchant, Nature (2020) https://doi.org/10.1038/d41586-020-00018-3

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(Multihead)
Self-attention
Feed-forward NN
Add + LayerNorm
Add + LayerNorm
Transformer
GNN Layer
Embedding + Pos Encoding
A Generalization of Transformer Networks to Graphs
Dwivedi & Bresson (2020) https://arxiv.org/abs/2012.09699
Do Transformers Really Perform Bad for Graph Representation?
Ying et al (2021) https://arxiv.org/abs/2106.05234
Communicative Representation Learning on Attributed Molecular Graphs
Song et al (2020) https://www.ijcai.org/proceedings/2020/0392.pdf
Graph-BERT: Only Attention is Needed for Learning Graph Representations
Zhang et al (2020) https://arxiv.org/abs/2001.05140
Veličković, Cucurull, Casanova, Romero, Liò, Bengio, Graph Attention Networks (ICLR 2018) https://arxiv.org/abs/1710.10903
Joshi, Transformers are Graph Neural Networks. (2020) https://graphdeeplearning.github.io/post/transformers-are-gnns/
Ying et al (2021) ͷGraphormer͸
KDDCup 2021ͷOpen Graph Benchmark
Large-Scale Challenge(‫ޙ‬ड़)ͷGraph-level
λεΫͷ༏উϞσϧͰ࢖ΘΕͨ
େ‫ن‬໛σʔλͳΒάϥϑͰ΋
Transformer͸༗ޮ…!?

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Strategies for Pre-training Graph Neural Networks
Hu, Liu, Gomes, Zitnik, Liang, Pande, Leskovec (ICLR 2020)
https://arxiv.org/abs/1905.12265
Self-Supervised Graph Transformer on Large-Scale Molecular Data
Rong, Bian, Xu, Xie, Wei, Huang, Huang (NeurIPS 2020)

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Zahrt, Henle, Rose, Wang, Darrow, Denmark,
Prediction of higher-selectivity catalysts by computer-driven
workﬂow and machine learning. Science, 363(6424), 2019.
https://doi.org/10.1126/science.aau5631

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https://youtu.be/uF53xsT7mjc
https://youtu.be/w6Pw4MOzMuo
ICLR 2021 Keynote (Michael Bronstein) Seminar Talk (Petar Veličković)

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N O
C
C
C
C
H
H
H
H
H
Dipole moment
Isotropic polarizability
HOMO energy
LUMO energy
Gap between HOMO and LUMO
Electronic spatial extent
Zero point vibrational energy
Internal energy at 0K
Internal energy at 298.15K
Enthalpy at 298.15K
Free energy at 298.15K
Heat capavity at 298.15K
Atomization energy at 0K
Atomization energy at 298.15K
Atomization enthalpy at 298.15K
Atomization free energy at 298.15K
Rotational constant A
Rotational constant B
Rotational constant C
ICML 2017 https://arxiv.org/abs/1704.01212 JCTC 2017 https://doi.org/10.1021/acs.jctc.7b00577

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1st place: 10 GNNs (12-Layer Graphormer) + 8 ExpC*s (5-Layer ExpandingConv)
73 GNNs (11-Layer LiteGEMConv with Self-Supervised Pretraining)
20 GNNs (32-Layer GNN with Noisy Nodes)
Test MAE 0.1200 (eV)
2nd place:Test MAE 0.1204 (eV)
3rd place: Test MAE 0.1205 (eV)
Results: https://ogb.stanford.edu/kddcup2021/results/#awardees_pcqm4m
https://ogb.stanford.edu/kddcup2021/

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• the number of immediate neighbors who are
“heavy” (non-hydrogen) atoms
• the valence minus the number of hydrogens
• the atomic number
• the atomic mass
• the atomic charge
• the number of attached hydrogens
• whether the atom is contained in at least one ring
• hydrogen-bond acceptor or not?
• hydrogen-bond donor or not?
• negatively ionizable or not?
• positively ionizable or not?
• aromatic or not?
• halogen or not?
Rogers and Hahn, JCIM (2005) https://doi.org/10.1021/ci100050t
Faber et al, JCTC (2017) https://doi.org/10.1021/acs.jctc.7b00577

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Continuous-Filter Convolutions
(cfconv layers)
<latexit sha1_base64="flzLPrMsSS6k1am7yfKyC95kal4=">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</latexit>
dij
rbf(γ,μ)
#rbf
MLP
dim of
element-wise product
Gaussian
Smearing
<latexit sha1_base64="CP/gGUdLE1ahITrVyosFmAESNpw=">AAAC5XichVHLThRBFL20KA8fjLIhcVNhAplZMKkBo4YV0Y0rw2uAhCJNdU/NTEFVV6e7egQ78wMm7owuXBhJXBg/wA8gIfwACz7B6A6FDQvu9HRilIi3012nzr3n9qm6XqhkbCk97nOu9V+/MTA4NHzz1u07I4W791Zik0S+qPlGmWjN47FQMhA1K60Sa2EkuPaUWPW2n3bzq20RxdIEy3Y3FBuaNwPZkD63SLmFTebpdKfjSsKUaFgeReYFYXGi3XSLMBkQprlt+Vylz7GoQ/JyzJm6sYSFLVliYicsTbEm15qTUt1N5VaHTKEyKZfLbqFIKzQLchlUc1CEPOZN4SswqIMBHxLQICAAi1gBhxifdagChRC5DUiRixDJLC+gA8OoTbBKYAVHdhu/Tdyt52yA+27POFP7+BeFb4RKAhP0iH6mJ/SQfqHf6Pk/e6VZj66XXVy9nlaE7sirsaWz/6o0rhZav1VXerbQgMeZV4new4zpnsLv6dsv350szS5OpJN0j35H/x/pMd3HEwTtn/6nBbH4/go/HnrBG8MBVf8ex2WwMl2pPqzMLDwozj3JRzUI92EcSjiPRzAHz2Aeatj/AH7ALzh1ms5r543ztlfq9OWaUfgjnA8XjcK2WA==</latexit>
xi
X
j2Ni
xj (exp( (dij µ)))
<latexit sha1_base64="sUht8Mvlx5JoWAMHabceBQWRmAs=">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</latexit>
xi
Schütt, Kindermans, Sauceda, Chmiela, Tkatchenko, Müller,
SchNet: A continuous-ﬁlter convolutional neural network for modeling quantum interactions. https://arxiv.org/abs/1706.08566

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Schütt et al, SchNet. (2017) https://arxiv.org/abs/1706.08566
Satorras et al, E(n) Equivariant Graph Neural Networks. (2021) https://arxiv.org/abs/2102.09844
Anderson et al, Cormorant. (2019) https://arxiv.org/abs/1906.04015
Unke et al, PhysNet. (2019) https://arxiv.org/abs/1902.08408
Klicpera et al, DimeNet++. (2020) https://arxiv.org/abs/2011.14115
Fuchs et al, SE(3)-Transformers. (2021) https://arxiv.org/abs/2006.10503
Köhler et al, Equivariant Flows (Radial Field). (2020) https://arxiv.org/abs/2006.02425
Thomas et al, Tensor Field Networks. (2018) https://arxiv.org/abs/1802.08219
<latexit sha1_base64="NH4UQ68bqmsH0AzQM//vHVYIu40=">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</latexit>
f(g · x) = g · f(x)
<latexit sha1_base64="z65vGkIR8AznuZeRro+w9TcH+xY=">AAACl3ichVHLSsNAFD3Gd3206kZxEyyVuilTFRVBLAri0qqtQislSac1mCYhmZZq8Qf8AReCoCAqfoAf4MYfcOEniMsKblx4mwZEi3rDZM6cuefOmbmqbeiuYOy5TWrv6Ozq7ukN9PUPDAZDQ8Np1yo7Gk9plmE5u6rickM3eUrowuC7tsOVkmrwHfVgtbG/U+GOq1vmtji0+V5JKZp6QdcUQVQuNFyIFrNa3hJydUpekgvR6lQuFGYx5oXcCuI+CMOPDSt0jyzysKChjBI4TAjCBhS49GUQB4NN3B5qxDmEdG+f4xgB0pYpi1OGQuwB/Yu0yvisSetGTddTa3SKQcMhpYwIe2K3rM4e2R17YR+/1qp5NRpeDmlWm1pu54Ino1vv/6pKNAvsf6n+9CxQwILnVSfvtsc0bqE19ZWj0/rW4makNsku2Sv5v2DP7IFuYFbetKsk3zz7w49KXujFqEHxn+1oBenpWHwuNpOcDSdW/Fb1YBwTiFI/5pHAOjaQovpVnOMaN9KYtCytSevNVKnN14zgW0jJT5AOlcI=</latexit>
f(g · x) = f(x)
<latexit sha1_base64="h5Nu57LzNEgsKVoc7SjFgDOfXxQ=">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</latexit>
g 2 G
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f : X ! Y

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NeurIPS 2020 ICML 2020, 2021
ICLR 2020, 2021
• Self-Supervised Graph Transformer on Large-Scale Molecular
Data
• RetroXpert: Decompose Retrosynthesis Prediction Like A
Chemist
• Reinforced Molecular Optimization with Neighborhood-
Controlled Grammars
• Autofocused Oracles for Model-based Design
• Barking Up the Right Tree: an Approach to Search over Molecule
Synthesis DAGs
• On the Equivalence of Molecular Graph Convolution and
Molecular Wave Function with Poor Basis Set
• CogMol: Target-Speciﬁc and Selective Drug Design for
COVID-19 Using Deep Generative Models
• A Graph to Graphs Framework for Retrosynthesis Prediction
• Hierarchical Generation of Molecular Graphs using Structural Motifs
• Learning to Navigate in Synthetically Accessible Chemical Space Using
Reinforcement Learning
• Reinforcement Learning for Molecular Design Guided by Quantum
Mechanics
• Multi-Objective Molecule Generation using Interpretable Substructures
• Improving Molecular Design by Stochastic Iterative Target
Augmentation
• A Generative Model for Molecular Distance Geometry
• GraphDF: A Discrete Flow Model for Molecular Graph Generation
• An End-to-End Framework for Molecular Conformation Generation via
Bilevel Programming
• Equivariant message passing for the prediction of tensorial properties
and molecular spectra
• Learning Gradient Fields for Molecular Conformation Generation
• Self-Improved Retrosynthetic Planning
• Directional Message Passing for Molecular Graphs
• GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation
• Augmenting Genetic Algorithms with Deep Neural Networks for Exploring the Chemical Space
• A Fair Comparison of Graph Neural Networks for Graph Classiﬁcation
• MARS: Markov Molecular Sampling for Multi-objective Drug Discovery
• Practical Massively Parallel Monte-Carlo Tree Search Applied to Molecular Design
• Learning Neural Generative Dynamics for Molecular Conformation Generation
• Conformation-Guided Molecular Representation with Hamiltonian Neural Networks
• Symmetry-Aware Actor-Critic for 3D Molecular Design

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https://arxiv.org/abs/2102.06321 https://arxiv.org/abs/1911.10084

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CC1CCNO1
Representation
Learning
…
Task-Speciﬁc
Head
https://itakigawa.github.io/data/aipseminar_202107.pdf
https://youtu.be/wtrVxZCXnPQ?t=813

(2021.7) 分子のグラフ表現と機械学習の最近

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